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alg-geom/9312006
An algorithmic criterion for basicness in dimension 2
We give a constructive procedure to check basicness of open (or closed) semialgebraic sets in a compact, non singular, real algebraic surface $X$. It is rather clear that if a semialgebraic set $S$ can be separated from each connected component of $X\setminus(S\cup\frz S)$ (when $\frz S$ stands for the Zariski closure ...
1993-12-14
2008-02-03
[ "alg-geom", "math.AG" ]
F. Acquistapace, F.Broglia, M.Pilar Velez
alg-geom/9312008
On the Hyperbolicity of the Complements of Curves in Algebraic Surfaces: The Three Component Case
The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a line and three quadrics. The main results are Let C be the union of three curves i...
1993-12-14
2014-12-01
[ "alg-geom", "math.AG" ]
Gerd Dethloff, Georg Schumacher, Pit-Mann Wong
alg-geom/9312007
Hyperbolicity of the complement of plane algebraic curves
The paper is a contribution of the conjecture of Kobayashi that the complement of a generic plain curve of degree at least five is hyperbolic. The main result is that the complement of a generic configuration of three quadrics is hyperbolic and hyperbolically embedded as well as the complement of two quadrics and a lin...
1993-12-14
2014-12-01
[ "alg-geom", "math.AG" ]
Gerd Dethloff, Georg Schumacher, Pit-Mann Wong
alg-geom/9312005
On the Hilbert Schemes of Canonically-Embedded Curves of Genus 5 and 6
A canonically-embedded curve of genus $g$ is a pure 1-dimensional, non-degenerate subscheme $C$ of ${\bf P}^{g-1}$ over an algebraically closed field $k$, for which ${\cal O}_C(1) \cong \omega_C$, (the dualizing sheaf)$ and $h^0(C, {\cal O}_C) = 1$, $h^0(C, \omega_C) = g$. The singularities of $C$ (if any) are Gorenste...
1993-12-10
2008-02-03
[ "alg-geom", "math.AG" ]
John Little
alg-geom/9312004
On Koszul property of the homogeneous coordinate ring of a curve
The following corollary has been added: for general tetragonal curve $C$ of genus $g\ge 9$ the homogeneous coordinate ring of $C$ defined by the line bundle $K(-T)$, where $K$ is the canonical class, $T$ is the tetragonal series, is Koszul. Also some misprints are corrected.
1993-12-08
2008-02-03
[ "alg-geom", "math.AG" ]
A. Polishchuk
alg-geom/9312003
Thickening Calabi-Yau moduli spaces
We describe a kind of deformation of the anti-DeRham algebra on a Calabi-Yau manifold $X$. These are in 1-1 correspondence with the total cohomology $\oplus H^i (X, \C)$.
1993-12-06
2008-02-03
[ "alg-geom", "math.AG" ]
Ziv Ran
alg-geom/9312001
The Functor of a Smooth Toric Variety
A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In this paper, we generalize this description to the case of maps from Y to an arbitrary smooth toric variety. The data needed to determine such a map consists of a collection of line bundles on Y together with a section of each line bundle. Further...
1993-12-03
2008-02-03
[ "alg-geom", "math.AG" ]
David A. Cox (Amherst College)
alg-geom/9312002
Complete ideals defined by sign conditions and the real spectrum of a two-dimensional local ring
This paper is about the local geometry of a real surfaces. It introduces machinery for studying families of subsets which are determined by conditions which are similar to base conditions, but also involve positivity/non-negativity. The methods used are the real spectrum and Zariski's theory of complete ideals.
1993-12-03
2008-02-03
[ "alg-geom", "math.AG" ]
Dean Alvis, Bernard Johnston, James Madden
alg-geom/9311013
Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds
Let B be a nef and big line bundle on a smooth complex threefold X with canonical bundle K. Let x be a point on X and suppose that BC\ge3 for any curve C passing x, B^2S\ge7 for any surface S containing x, and B^3\ge51. Then K+B is spanned at x. (Ein-Lazarsfeld proved the assertion assuming B^3\ge92.) Corollary: K+3L i...
1993-11-30
2008-02-03
[ "alg-geom", "math.AG" ]
Takao Fujita (Tokyo Inst. of Tech.)
alg-geom/9311011
On the Brauer Group of Real Algebraic Surfaces
Let X be a real projective algebraic manifold, s numerates connected components of X(R) and _2Br(X) the subgroup of elements of order 2 of the cohomological Brauer group Br(X). We study the natural homomorphism \xi : _2Br(X) \to (Z/2)^s and prove that \xi is epimorphic if H^3(X(C)/G;Z/2) \to H^3(X(R);Z/2) is injective....
1993-11-28
2008-02-03
[ "alg-geom", "math.AG" ]
Viacheslav V. Nikulin
alg-geom/9311010
On Brauer Groups of Real Enriques Surfaces
Let Y be a real Enriques surface, _2Br(Y) the subgroup of elements of order 2 of Br(Y), and s, s_{or}, and s_{nor} the number of all connected, connected orientable, and connected non-orientable components of Y(R) respectively. Using universal covering K3-surface X of Y, we connect dim _2Br(Y) with the s, s_{or} and s_...
1993-11-28
2008-02-03
[ "alg-geom", "math.AG" ]
V. V. Nikulin and R. Sujatha
alg-geom/9311012
On the Topological Classification of Real Enriques Surfaces. I
This note contains preliminary calculation of topological types or real Enriques surfaces. We realize 59 topological types of real Enriques surfaces (Theorem 6) and show that all other topological types belong to the list of 21 topological types (Theorem 7). In fact, our calculation contains much more information which...
1993-11-28
2008-02-03
[ "alg-geom", "math.AG" ]
Viacheslav V. Nikulin
alg-geom/9311008
Spin polynomial invariants for Dolgachev surfaces
We consider the spin polynomial invariants for bundles with c_2=2 and c_1 = K_S + 2nk a rational mutiple of the canonical divisor on a Dolgacev surface. It is shown that the chamber structure can be controlled so that the polynomials give diffeomorphism invariants of Dolgachev surfaces of the form q_S(n) = a(n)Q^2 + b(...
1993-11-23
2008-02-03
[ "alg-geom", "math.AG" ]
S. Bauer and V. Pidstrigatch
alg-geom/9311007
On the Picard Number of Fano 3-Folds with Terminal Singularities
We prove the following main result: Let X be a Fano 3-fold with terminal Q-factorial singularities and X does not have a small extremal ray and a face of Kodaira dimension 1 or 2 for Mori polyhedron of X. Then the Picard number \rho (X) < 8.
1993-11-19
2008-02-03
[ "alg-geom", "math.AG" ]
Viacheslav V. Nikulin
alg-geom/9311006
Surfaces of Degree 10 in the Projective Fourspace via Linear Systems and Linkage
The paper discusses the classification of surfaces of degree 10 and sectional genus 9 and 10. The surfaces of degree at most 9 are described through classical work dating from the last century up to recent years, while surfaces of degree 10 and other sectional genera are studied elsewhere. We use relations between mu...
1993-11-16
2008-02-03
[ "alg-geom", "math.AG" ]
Sorin Popescu and Kristian Ranestad
alg-geom/9311005
Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces
Let $S$ be a birationally ruled surface. We show that the moduli schemes $M_S(r,c_1,c_2)$ of semistable sheaves on $S$ of rank $r$ and Chern classes $c_1$ and $c_2$ are irreducible for all $(r,c_1,c_2)$ provided the polarization of $S$ used satisfies a simple numerical condition. This is accomplished by proving that th...
1993-11-16
2008-02-03
[ "alg-geom", "math.AG" ]
Charles Walter
alg-geom/9311004
On discrete Zariski-dense subgroups of algebraic groups
We investigate for which linear-algebraic groups (over the complex numbers or any local field) there exists subgroups which are dense in the Zariski topology, but discrete in the Hausdorff topology. For instance, such subgroups exist for every non-solvable complex group.
1993-11-14
2008-02-03
[ "alg-geom", "math.AG" ]
J. Winkelmann
alg-geom/9311003
Geometric height inequality on varieties with ample cotangent bundles
Let F be a function field of one variable over an algebraically closed field of characteristic zero, X a geometrically irreducible smooth projective variety over F, and L a line bundle on X. In this note, we will prove that if the contangent bundle of X is ample and X is non-isotrivial, then there are a proper closed a...
1993-11-10
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9311002
Projective Degenerations of K3 Surfaces, Gaussian Maps, and Fano Threefolds
In this article we exhibit certain projective degenerations of smooth $K3$ surfaces of degree $2g-2$ in $\Bbb P^g$ (whose Picard group is generated by the hyperplane class), to a union of two rational normal scrolls, and also to a union of planes. As a consequence we prove that the general hyperplane section of such $K...
1993-11-09
2009-10-22
[ "alg-geom", "math.AG" ]
Ciro Ciliberto, Angelo Lopez, and Rick Miranda
alg-geom/9311001
On Banica sheaves and Fano manifolds
In the present paper we discuss coherent sheaves of rank > 1 whose projectivization gives rise to smooth varieties - varieties of this type are also called smooth scrolls. We prove some basic properties of these varieties and we give some pertinent examples. We classify Fano manifolds of large index which are of this t...
1993-11-07
2008-02-03
[ "alg-geom", "math.AG" ]
Edoardo Ballico and Jaroslaw Wisniewski
alg-geom/9310008
A Propos de l'Existence de Fibr\'es Stables sur les Surfaces
We prove the existence (in characteristic 0) on every polarized (smooth, projective and connected) surface of stable bundles of rank $r\geq 2$, arbitrary first Chern class and large enough $c_2$.
1993-10-29
2008-02-03
[ "alg-geom", "math.AG" ]
Andr\'e Hirschowitz, Yves Laszlo
alg-geom/9310007
Initial ideals, Veronese subrings, and rates of algebras
We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take d sufficiently large, say at least half the regularity of the ideal defining the...
1993-10-11
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
David Eisenbud, Alyson Reeves, and Burt Totaro
alg-geom/9310005
Teichm\"uller Theory and the Universal Period Mapping via Quantum Calculus and the $H^{1/2}$ Space on the Circle
The Universal Teichm\"uller Space, $T(1)$, is a universal parameter space for all Riemann surfaces. In earlier work of the first author it was shown that one can canonically associate infinite- dimensional period matrices to the coadjoint orbit manifold $Diff(S^1)/Mobius(S^1)$ -- which resides within $T(1)$ as the (Kir...
1993-10-07
2008-02-03
[ "alg-geom", "funct-an", "hep-th", "math.AG", "math.FA" ]
Subhashis Nag and Dennis Sullivan
alg-geom/9310006
Torsion Sections of Elliptic Surfaces
Given a torsion section of a semistable elliptic surface, we prove equidistribution results for the components of singular fibers which are hit by the section, and for the root of unity (identifying the zero component with ${\Bbb C}$) which is hit by the section in case the section hits the zero component.
1993-10-07
2008-02-03
[ "alg-geom", "math.AG" ]
Rick Miranda and Peter F. Stiller
alg-geom/9310002
General hyperplane sections of nonsingular flops in dimension 3
We give a simple proof of a theorem of Katz and Morrison.
1993-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Yujiro Kawamata
alg-geom/9310004
Quantum Cohomology Rings of Toric Manifolds
We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of an arbitrary $d$-dimensional smooth projective toric manifold ${\bf P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of $H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ depends on the choice of an element $avarphi$ in the ord...
1993-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Victor V. Batyrev
alg-geom/9310003
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed $n$-dimensional Newton polyhedron $\Delta$ in $n$-dimensional algebraic torus ${\bf T} =({\bf C}^*)^n$. ...
1993-10-05
2008-02-03
[ "alg-geom", "math.AG" ]
Victor V. Batyrev
alg-geom/9310001
Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties
We propose a combinatorical duality for lattice polyhedra which conjecturally gives rise to the pairs of mirror symmetric families of Calabi-Yau complete intersections in toric Fano varieties with Gorenstein singularities. Our construction is a generalization of the polar duality proposed by Batyrev for the case of hyp...
1993-10-02
2008-02-03
[ "alg-geom", "math.AG" ]
Lev Borisov
alg-geom/9309007
The Monomial-Divisor Mirror Map
For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural construction of the isomorphism between certain Hodge groups of these hypersurfaces, as predicted by mirror symmetry, which we call th...
1993-09-30
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Paul S. Aspinwall, Brian R. Greene and David R. Morrison
alg-geom/9309006
Conic bundles in projective fourspace
P. Ellia and G.Sacchiero have shown that if $S$ is a smooth surface in $\Pn 4$ which is ruled in conics, then $S$ has degree 4 or 5. In this paper we give a proof of this result combining the ideas of Ellia and Sacchiero as they are used in the paper of the second author on plane curve fibrations and the recent work of...
1993-09-27
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Braun and Kristian Ranestad
alg-geom/9309005
Differential-geometric methods for the lifting problem and linear systems on plane curves
Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the homogeneous ideal of $X$ is studied. A conjecture is given in terms of $d$, $r$ and ...
1993-09-23
2008-02-03
[ "alg-geom", "math.AG" ]
Emilia Mezzetti
alg-geom/9309004
Generic Singularities of Holomorphic Foliations
A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the singular set is one less than the leaf dimension. In this article we study the genera...
1993-09-21
2008-02-03
[ "alg-geom", "math.AG" ]
Sinan Sertoz
alg-geom/9309003
Conformal blocks and generalized theta functions
Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global sections of L^k with a space known in conformal field theory as the ``space of conf...
1993-09-15
2009-10-22
[ "alg-geom", "math.AG" ]
Arnaud Beauville and Yves Laszlo
alg-geom/9309002
A family of \'etale coverings of the affine line
In the note we construct a family of \'etale coverings of the affine line. More specifically, let $F$ be a finite field of characteristic $p$ and suppose that the cardinality of $F$ is at least 4. Let $A = F[T]$ be the polynomial ring in one variable $T$, $K=F(T)$. Let $K_\infty$ be the completion of $K$ along the valu...
1993-09-02
2015-06-30
[ "alg-geom", "math.AG" ]
Kirti Joshi (School of Mathematics, Tata Institute of Fundamental Research, Bombay)
alg-geom/9309001
Theoremes de connexites et varietes abeliennes
We prove a connexity theorem for abelian varieties in characteristic $0$: if $X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$ over $X$ is connected. This theorem has several consequences: the algebraic fundamental groups ...
1993-09-01
2008-02-03
[ "alg-geom", "math.AG" ]
Olivier Debarre
alg-geom/9308006
Unobstructedness of Calabi-Yau OrbiKleinfolds
We show that Calabi-Yau spaces with certain types of hypersurface- quotient singularities have unobstructed deformations. This applies in particular to all Calabi-Yau orbifolds nonsingular in codimension 2.
1993-08-31
2008-02-03
[ "alg-geom", "math.AG" ]
Z. Ran
alg-geom/9308005
The existence of higher logarithms
In this paper we prove the existence of all higher logarithms as multivalued and ordinary Deligne cohomology classes.
1993-08-31
2008-02-03
[ "alg-geom", "math.AG" ]
Richard Hain
alg-geom/9308004
Vector bundles and $SO(3)$ invariants for elliptic surfaces III: The case of odd fiber degree
This paper, the last in a series of three, studies vector bundles on an elliptic surface whose determinant has odd intersection number with a general fiber and uses this study to calculate certain coefficients of Donaldson polynomials.
1993-08-23
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Friedman
alg-geom/9308003
Some remarks on the Kronheimer-Mrowka classes of algebraic surfaces
Define the Donaldson series of a simply connected 4-manifold by q(X) = \sum_d q_d(X)/d! Recently Kronheimer and Mroka have announced the result that the Donaldson series of so called simple 4-manifolds can be written as q(X) = e^{Q/2}\sum_{i=1}^p a_i e^{K_i} where $Q$ is the intersection form and the $K_i \in H...
1993-08-20
2008-02-03
[ "alg-geom", "math.AG" ]
R. Brussee
alg-geom/9308002
The Euler Series of Restricted Chow Varieties
Let X be an algebraic projective variety in {\bf P}^n. Denote by {\cal C}_{\lambda} the space of all effective cycles on X whose homology class is \lambda \in H_{2p} (X,{\bf Z}). It is easy to show that {\cal C}_{\lambda} is an algebraic projective variety. Let \chi ({\cal C}_{\lambda} be its Euler characteristic. Defi...
1993-08-11
2008-02-03
[ "alg-geom", "math.AG" ]
Javier Elizondo
alg-geom/9308001
On the Griffiths group of the cubic sevenfold
We prove that the Griffiths group of 3-cycles homologous to zero modulo algebraic equivalence, on a generic hypersurfaces of dimension 7 and degree 3 is not finitely generated, even when tensored with Q. Using this and a result of Nori, we give examples of varieties for which some Griffiths group is not finitely genera...
1993-08-03
2008-02-03
[ "alg-geom", "math.AG" ]
Alberto Albano and Alberto Collino
alg-geom/9307010
Generalized Hypergeometric Functions and Rational Curves on Calabi-Yau Complete Intersections in Toric Varieties
We formulate general conjectures about the relationship between the A-model connection on the cohomology of a $d$-dimensional Calabi-Yau complete intersection $V$ of $r$ hypersurfaces $V_1, \ldots, V_r$ in a toric variety ${\bf P}_{\Sigma}$ and the system of differential operators annihilating the special hypergeometri...
1993-07-30
2009-10-22
[ "alg-geom", "math.AG" ]
Victor V. Batyrev and Duco van Straten
alg-geom/9307009
Hyperkaehler and holomorphic symplectic geometry
We prove that all complex analytic subvarieties of a generic compact hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are holomorphically symplectic.
1993-07-29
2008-02-03
[ "alg-geom", "math.AG" ]
Misha Verbitsky
alg-geom/9307008
Hyperholomorphic bundles
Hyperholomorphic bundle is a bundle with connection defined over a hyperkaehler manifold such that this connection is holomorphic with respect to all complex structures induced by a hyperkaehler structure. A hyperholomorphic connection is Yang-Mills. If a stable bundle has first two Chern classes invariant with respect...
1993-07-29
2008-02-03
[ "alg-geom", "math.AG" ]
Misha Verbitsky
alg-geom/9307006
Boundary of the Picard Group of a Singular Curve
In this work we explore the boundary of the jacobian of a singular curve in the compactified picard group. We formulate a functor that helps to determine this boundary and show that this functor is representable. We try to dertermine the points on the boundary.
1993-07-24
2008-02-03
[ "alg-geom", "math.AG" ]
Jyotsna Gokhale
alg-geom/9307007
Compactified Jacobian of some Singular Curves
We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.
1993-07-24
2008-02-03
[ "alg-geom", "math.AG" ]
Jyotsna Gokhale
alg-geom/9307005
Duistermaat-Heckman measures in a non-compact setting
We prove a \dh type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain the classical analogues of well-known multiplicity formulas for the holomor...
1993-07-21
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Elisa Prato and Siye Wu
alg-geom/9307004
Arithmetic Bogomolov-Gieseker's inequality
Let f : X --> Spec(Z) be an arithmetic variety of dimension d >= 2 and (H, k) an arithmetically ample Hermitian line bundle on X. Let (E, h) be a rank r vector bundle on X. In this paper, we will prove that if E is semistable with respect to H on each connected component of the infinite fiber of X, then { c_2(E, h) -...
1993-07-19
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9307002
Vector bundles and $SO(3)$ invariants for elliptic surfaces I
This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney class is transverse to the unique primitive class $\kappa$ such that a positive ...
1993-07-14
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Friedman
alg-geom/9307003
Vector bundles and $SO(3)$ invariants for elliptic surfaces II: The case of even fiber degree
This paper is the second in a series of three devoted to the smooth classification of simply connected elliptic surfaces. In this paper, we study the case where one of the multiple fibers has even multiplicity, and describe the moduli space of stable rank two vector bundles with the appropriate first Chern class needed...
1993-07-14
2008-02-03
[ "alg-geom", "math.AG" ]
Robert Friedman
alg-geom/9307001
Localization for nonabelian group actions
Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group $K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $\mu: X \to {\rm Lie}(K)^*$ and Marsden-Weinstein reduction $\xred = \mu^{-1}(0)/K$. There is then a natural surjective map $\kappa_0$ from the equivariant cohomology $H^*...
1993-07-06
2008-02-03
[ "alg-geom", "math.AG" ]
L.C. Jeffrey and F.C. Kirwan
alg-geom/9306011
On the Hodge Structure of Projective Hypersurfaces in Toric Varieties
This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric variety $P$ and an ample hypersurface $X$ defined by an polynomial $f$ in the homogeneous coordinate ring $S$ of $P$ (as d...
1993-06-25
2008-02-03
[ "alg-geom", "math.AG" ]
Victor V. Batyrev (Essen) and David A. Cox (Amherst College)
alg-geom/9306009
Classification of smooth congruences with a fundamental curve
We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve contained in $G(1,n)$.
1993-06-23
2008-02-03
[ "alg-geom", "math.AG" ]
Enrique Arrondo, Marina Bertolini and Cristina Turrini
alg-geom/9306010
On stability of tangent bundles of Fano manifolds with b_2=1
In the present paper we discuss stability of the tanget bundle of a Fano n-fold of index >= n-2 and b_2=1. For example, we prove that all Fano 4-folds with b_2=1 have stable tangent bundle. For this purpose we prove some vanishing theorems for sheaves of twisted holomorphic forms on ample divisors and cyclic coverings ...
1993-06-22
2008-02-03
[ "alg-geom", "math.AG" ]
Thomas Peternell, Jaroslaw A. Wisniewski
alg-geom/9306008
Distribution of Energy Levels of a Quantum Free Particle on a Surface of Revolution
We prove that the error term $\La(R)$ in the Weyl asymptotic formula $$\#\{ E_n\le R^2\}={\Vol M\over 4\pi} R^2+\La(R),$$ for the Laplace operator on a surface of revolution $M$ satisfying a twist hypothesis, has the form $\La(R) =R^{1/2}F(R)$ where $F(R)$ is an almost periodic function of the Besicovitch class $B^2$, ...
1993-06-18
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Pavel Bleher
alg-geom/9306007
Trisecant Lines And Jacobians, II
Let $\Theta$ be a symmetric theta divisor on an indecomposable principally polarized complex abelian variety $X$. The linear system $|2\Theta |$ defines a morphism $K:X\ra |2\Theta |^*$, whose image is the Kummer variety $K(X)$ of $X$. When $(X,\theta)$ is the Jacobian of an algebraic curve, there are infinitely many t...
1993-06-18
2008-02-03
[ "alg-geom", "math.AG" ]
Olivier Debarre
alg-geom/9306006
Bogomolov Instability and Kawamata-Viehweg Vanishing
The purpose of this note is to show how the Kawamata-Viehweg vanishing theorem for fractional divisors leads to a quick new proof of Bogomolov's instability theorem for rank two vector bundles on an algebraic surface.
1993-06-17
2008-02-03
[ "alg-geom", "math.AG" ]
Guillermo Fernandez del Busto
alg-geom/9306005
Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective scheme and is dominated by the algebraic compactification arising as a Grothendieck Quot scheme. The latt...
1993-06-08
2008-02-03
[ "alg-geom", "math.AG" ]
Aaron Bertram, Georgios Daskalopoulos, Richard Wentworth
alg-geom/9306004
Very ample linear systems on abelian varieties
Let $(X,L)$ be a polarized complex abelian variety of dimension $g$ where $L$ is a polarization of type $(1,...,1,d)$. For $(X,L)$ genberic we prove the following: (1) If $d \ge g+2$, then $\phi_L\colon X \to {\bf P}^{d-1}$ defines a birational morphism onto its image. (2) If $d > 2^g$, then $L$ is very ample. We...
1993-06-04
2008-02-03
[ "alg-geom", "math.AG" ]
O. Debarre, K. Hulek, J. Spandaw
alg-geom/9306003
Linear Structure on Calabi-Yau Moduli Spaces
We show that the formal moduli space of a Calabi-Yau manifold $X^n$ carries a linear structure, as predicted by mirror symmetry. This linear structure is canonically associated to a splitting of the Hodge filtration on $H^n(X)$.
1993-06-03
2008-02-03
[ "alg-geom", "math.AG" ]
Z. Ran
alg-geom/9306001
The automorphism group of the moduli space of semi stable vector bundles
Let ${\cal S}{\cal U}(r, L_0)$ denote the moduli space of semi stable vector bundles of rank $r$ and fixed determinant $L_0$ of degree $d$ on a smooth curve $C$ of genus $g \geq 3$. In this paper we describe the group of automorphisms of $ {\cal S}{\cal U}(r, L_0) $. The analogue of this result is carried out for the s...
1993-06-02
2008-02-03
[ "alg-geom", "math.AG" ]
Alexis Kouvidakis and Tony Pantev
alg-geom/9306002
Picard groups of Hilbert schemes of curves
We calculate the Picard group, over the integers, of the Hilbert scheme of smooth, irreducible, non-degenerate curves of degree $d$and genus $g \geq 4$ in ${\Bbb P}^r$, in the case when $d \geq 2g+1 $ and $r \leq d-g$. We express the classes of the generators in terms of some ``natural'' divisor classes.
1993-06-02
2008-02-03
[ "alg-geom", "math.AG" ]
Alexis Kouvidakis
alg-geom/9305012
A Kaehler Structure on the Space of String World-Sheets
Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with fixed boundary conditions. Then the infinite-dimensional manifold S carries a natural complex structure and a compatible (positive-definite) Kaehler metric h on S de...
1993-05-26
2009-10-22
[ "alg-geom", "math.AG" ]
Claude LeBrun
alg-geom/9305010
Finding Sparse Systems of Parameters
For several computational procedures such as finding radicals and Noether normalizations, it is important to choose as sparse as possible a system of parameters in a polynomial ideal or modulo a polynomial ideal. We describe new strategies for these tasks, thus providing solutions to problems (1) and (2) posed in [Eise...
1993-05-20
2008-02-03
[ "alg-geom", "math.AC", "math.AG" ]
David Eisenbud and Bernd Sturmfels
alg-geom/9305011
On the fundamental group of an abelian cover
We study the behaviour of the topological fundamental group under totally ramified abelian covers (a special case of abelian Galois covers) of complex projective varieties of dimension at least 2.
1993-05-20
2008-02-03
[ "alg-geom", "math.AG" ]
Rita Pardini, Francesca Tovena
alg-geom/9305007
An inequality for polynomial mappings
We give an estimate of the growth of a polynonial mapping of $C^n$.
1993-05-19
2016-08-14
[ "alg-geom", "math.AG" ]
Arkadiusz P{\l}oski
alg-geom/9305008
Injectivity on one line
Let $k$ be an algebraically closed field of characteristic zero. Let $H:k^2\to k^2$ be a polynomial mapping such that the Jacobian $\text{Jac}\,H$ is a non-zero constant. In this note we prove, that if there is a line $l \subset k^2$ such that $H|_l:l\to k^2$ is an injection, then $H$ is a polynomial automorphism.
1993-05-19
2016-08-14
[ "alg-geom", "math.AG" ]
Janusz Gwo\'zdziewicz
alg-geom/9305006
The Noether exponent and Jacobi formula
For any polynomial mapping $F=(F_1,\dots ,F_n)$ of $\Cal C^n$ with a finite number of zeros we define the Noether exponent $\nu(F)$. We prove the Jacobi formula for all polynomials of degree strictly less than $\sum_{i=1}^n (\deg F_i-1)-\nu(F)$.
1993-05-19
2016-08-14
[ "alg-geom", "math.AG" ]
Arkadiusz P{\l}oski
alg-geom/9305009
On the approximate roots of polynomials
We give a simplified approach to the Abhyankar--Moh theory of approximate roots. Our considerations are based on properties of the intersection multiplicity of local curves.
1993-05-19
2016-08-14
[ "alg-geom", "math.AG" ]
Janusz Gwo\'zdziewicz and Arkadiusz P{\l}oski
alg-geom/9305005
Inequality of Bogomolov-Gieseker's type on arithmetic surfaces
Let K be an algebraic number field, O_K the ring of integers of K, and f : X --> Spec(O_K) an arithmetic surface. Let (E, h) be a rank r Hermitian vector bundle on X such that $E$ is semistable on the geometric generic fiber of f. In this paper, we will prove an arithmetic analogy of Bogomolov-Gieseker's inequality: c_...
1993-05-12
2008-02-03
[ "alg-geom", "math.AG" ]
Atsushi Moriwaki
alg-geom/9305004
Kodaira energies of polarized log varieties
Let L be an ample line bundle on a log variety (V, D) having only log terminal singularities.The Kodaira energy of such a triple (V, D, L) is defined as follows: \kappa\epsilon=-Inf{t\in Q | K(V,D)+tL is big}. Here K(V,D)=K_V+D is the log canonical bundle of (V,D) and "big" means \kappa=dim V. We first show that the ra...
1993-05-07
2008-02-03
[ "alg-geom", "math.AG" ]
T. Fujita
alg-geom/9305003
Log contractions and equidimensional models of elliptic threefolds
This work was initially motivated by Miranda's work on elliptic Weierstrass threefolds. Miranda [Mi] describes a smooth equidimensional (flat) model for any elliptic Weierstrass threefold; such models occur naturally in the study of moduli spaces. In this paper we use minimal model theory to link birational maps of log...
1993-05-05
2008-02-03
[ "alg-geom", "math.AG" ]
A. Grassi
alg-geom/9305002
A Finiteness Theorem for Elliptic Calabi-Yau Threefolds
We prove that up to birational equivalence, there exists only a finite number of families of Calabi-Yau threefolds (i.e. a threefold with trivial canonical class and factorial terminal singularities) which have an elliptic fibration to a rational surface. This strengthens a result of B. Hunt that there are only a finit...
1993-05-03
2008-02-03
[ "alg-geom", "math.AG" ]
M. Gross
alg-geom/9305001
A General Noether-Lefschetz Theorem and applications
In this paper we generalize the classical Noether-Lefschetz Theorem to arbitrary smooth projective threefolds. Let $X$ be a smooth projective threefold over complex numbers, $L$ a very ample line bundle on $X$. Then we prove that there is a positive integer $n_0(X,L)$ such that for $n \geq n_0(X,L)$, the Noether-Lefsch...
1993-05-03
2024-07-09
[ "alg-geom", "math.AG" ]
Kirti Joshi
alg-geom/9304007
Compactifications of moduli spaces inspired by mirror symmetry
We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds, using the one-loop semiclassical approximation. The data being parameterized includes a choice of complex structure on the manifold, as well as some ``extra structure'' described by means of classes in H^2. The expectation that this moduli space ...
1993-04-23
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
David R. Morrison
alg-geom/9304006
Recovering of curves with involution by extended Prym data
With every smooth, projective algebraic curve $\tilde{C}$ with involution $\sigma :\tilde{C}\longrightarrow \tilde{C}$ without fixed points is associated the Prym data which consists of the Prym variety $P:=(1-\sigma )J(\tilde{C})$ with principal polarization $\Xi$ such that $2\Xi$ is algebraically equivalent to the re...
1993-04-14
2008-02-03
[ "alg-geom", "math.AG" ]
Vassil Kanev
alg-geom/9304005
Schur quadrics, cubic surfaces and rank 2 vector bundles over the projective plane
A cubic surface in $P^3$ is known to contain 27 lines, out of which one can form 36 Schlafli double - sixes i.e., collections $l_1,...,l_6, l'_1,..., l'_6\}$ of 12 lines such that each $l_i$ meets only $l'_j, j\neq i$ and does not meet $l_j, j\neq i$. In 1881 F. Schur proved that any double - six gives rise to a certai...
1993-04-13
2008-02-03
[ "alg-geom", "math.AG" ]
I. Dolgachev and M. Kapranov
alg-geom/9304004
Holomorphic Slices, Symplectic Reduction and Multiplicities of Representations
I prove the existence of slices for an action of a reductive complex Lie group on a K\"ahler manifold at certain orbits, namely those orbits that intersect the zero level set of a momentum map for the action of a compact real form of the group. I give applications of this result to symplectic reduction and geometric qu...
1993-04-12
2008-02-03
[ "alg-geom", "math.AG" ]
Reyer Sjamaar
alg-geom/9304003
What can be computed in algebraic geometry?
This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic introduction to Grobner bases. 3. Bounds in algebraic geometry, and regularity an...
1993-04-11
2015-06-30
[ "alg-geom", "math.AG" ]
Dave Bayer and David Mumford
alg-geom/9304002
Refined intersection products and limiting linear subspaces of hypersurfaces
Let $X$ be a hypersurface of degree $d$ in $\Bbb P^n$ and $F_X$ be the scheme of $\Bbb P^r$'s contained in $X$. If $X$ is generic, then $F_X$ will have the expected dimension (or empty) and its class in the Chow ring of $G(r+1,n+1)$ is given by the top Chern class of the vector bundle $S^dU^*$, where $U$ is the univers...
1993-04-07
2008-02-03
[ "alg-geom", "math.AG" ]
Xian Wu
alg-geom/9304001
Birational Equivalences of Vortex Moduli
We construct a finite dimensional Kaehler manifold with a holomorphic, symplectic circle action whose symplectic reduced spaces may be identified with the tau-vortex moduli spaces (or tau-stable pairs). The Morse theory of the circle action induces natural birational maps between the reduced spaces for different values...
1993-04-06
2008-02-03
[ "alg-geom", "math.AG" ]
S. Bradlow, G. Daskalopoulos, and R. Wentworth
alg-geom/9303007
The Variety of Positive Superdivisors of a Supercurve (Supervortices)
The supersymmetric product of a supercurve is constructed with the aid of a theorem of algebraic invariants and the notion of positive relative superdivisor (supervortex) is introduced. A supercurve of positive superdivisors of degree 1 (supervortices of vortex number 1) of the original supercurve is constructed as its...
1993-03-29
2008-02-03
[ "alg-geom", "math.AG" ]
J.A. Dominguez Perez, D. Hernandez Ruiperez and C. Sancho de Salas
alg-geom/9303005
Free pencils on divisors
Let X be a smooth projective variety defined over an algebraically closed field, and let Y in X be a reduced and irreducible ample divisor in X. We give a numerical sufficient condition for a base point free pencil on $Y$ to be the restriction of a base point free pencil on $X$. This result is then extended to families...
1993-03-28
2008-02-03
[ "alg-geom", "math.AG" ]
Roberto Paoletti
alg-geom/9303006
Seshadri constants, gonality of space curves and restriction of stable bundles
We define the Seshadri constant of a space curve and consider ways to estimate it. We then show that it governs the gonality of the curve. We use an argument based on Bogomolov's instability theorem on a threefold. The same methods are then applied to the study of the behaviour of a stable vector bundle on P^3 under re...
1993-03-28
2008-02-03
[ "alg-geom", "math.AG" ]
Roberto Paoletti
alg-geom/9303004
Theta Functions for $\SL(n)$ versus $\GL(n)$
Over a smooth complex projective curve $C$ of genus $g$ let $\M (n,d)$ be the moduli space of semistable bundles of rank $n$ and degree $d$ on $C$, and $\SM (n,L)$, the moduli space of those bundles whose determinant is isomorphic to a fixed line bundle $L$ over $C$. Let $\theta_F$ and $\theta$ be theta bundles over th...
1993-03-28
2008-02-03
[ "alg-geom", "math.AG" ]
Ron Donagi and Loring W. Tu
alg-geom/9303003
Deformations of cones over hyperelliptic curves
We determine the versal deformation of cones, in the simplest case: cones over hyperelliptic curves of high degree. In particular, we show that for degree $4g+4$, the highest degree for which interesting deformations exist, the number of smoothing components is $2^{2g+1}$ ($g\neq3$). We review in a general setting th...
1993-03-23
2015-06-30
[ "alg-geom", "math.AG" ]
Jan Stevens
alg-geom/9303002
Projective varieties with many degenerate subvarieties
We study the problem of classifying the irreducible projective varieties $X$ of dimension $n\ge 2$ in $\Bbb P^N$ which contain an algebraic family $\Cal F$ of dimension $h+1$ ($h<n$) of subvarieties $Y$ of dimension $n-h$, each one contained in a $\Bbb P^{N-h-1}$. We prove that one of the following happens: (i) there e...
1993-03-20
2008-02-03
[ "alg-geom", "math.AG" ]
Emilia Mezzetti
alg-geom/9303001
Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic
We extend the minimal model theorem to the 3-dimensional schemes which are projective and have semistable reduction over the spectrum of a Dedekind ring.
1993-03-05
2008-02-03
[ "alg-geom", "math.AG" ]
Yujiro Kawamata
alg-geom/9302006
Existence and Deformation Theory for Scalar-Flat Kaehler Metrics on Compact Complex Surfaces
Let M be a compact complex surface which admits a Kaehler metric whose scalar curvature has integral zero; and suppose the fundamental group of M does not contain an Abelian subgroup of finite index. Then if M is blown up at sufficiently many points, the resulting surface M' admits scalar-flat Kaehler metrics.
1993-02-23
2009-10-22
[ "alg-geom", "math.AG" ]
Claude LeBrun and Michael Singer
alg-geom/9302005
A Finiteness Theorem for Quaternionic-Kaehler Manifolds with Positive Scalar Curvature
We study the topology and geometry of those compact Riemannian (4n)-manifolds (M,g), n > 1, with positive scalar curvature and holonomy in Sp(n)Sp(1). Up to homothety, we show that there are only finitely many such manifolds of any dimension 4n.
1993-02-23
2008-02-03
[ "alg-geom", "math.AG" ]
Claude LeBrun
alg-geom/9302004
Intersection homology Betti numbers
A generalization of the formula of Fine and Rao for the ranks of the intersection homology groups of a complex algebraic variety is given. The proof uses geometric properties of intersection homology and mixed Hodge theory.
1993-02-12
2008-02-03
[ "alg-geom", "math.AG" ]
Alan H. Durfee
alg-geom/9302003
Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes
A simple convex lattice polytope $\Box$ defines a torus-equivariant line bundle $\LB$ over a toric variety $\XB.$ Atiyah and Bott's Lefschetz fixed-point theorem is applied to the torus action on the $d''$-complex of $\LB$ and information is obtained about the lattice points of $\Box$. In particular an explicit formula...
1993-02-09
2008-02-03
[ "alg-geom", "math.AG" ]
Sacha Sardo-Infirri
alg-geom/9302002
On the surjectivity of Wahl maps on a general curve
This paper explores the geometric meaning of the failure of certain kinds of Wahl maps to surject on a general curve. Sufficient conditions for surjectivity are given. An approach used by Voisin to study canonical Wahl maps is applied in this direction.
1993-02-09
2008-02-03
[ "alg-geom", "math.AG" ]
Roberto Paoletti
alg-geom/9302001
A note on non-vanishing and applications
Let $X$ be a normal variety over the field of complex numbers with log terminal singularities and the canonical divisor $K_X$ being ${\bf Q}$-Gorenstein. Assume that $L$ is an ample line bundle over $X$ and $\phi: X\to Y$ is a morphism supported by $K_X+rL$ for some positive rational number $r$. In the present paper we...
1993-02-01
2008-02-03
[ "alg-geom", "math.AG" ]
Marco Andreatta, Jaros{\l}aw A. Wi\'sniewski
alg-geom/9301007
Bounds of automorphism groups of genus 2 fibrations
For a complex surface of general type with a relatively minimal genus 2 fibration, the bounds of the orders of the automorphism group of the fibration, of its abelian subgroups and of its cyclic subgroups are determined as linear functions of $c^2_1$. Most of them are the best.
1993-01-29
2008-02-03
[ "alg-geom", "math.AG" ]
Zhi-Jie Chen
alg-geom/9301006
Rational curves on Calabi-Yau manifolds: verifying predictions of Mirror Symmetry
Mirror symmetry, a phenomenon in superstring theory, has recently been used to give tentative calculations of several numbers in algebraic geometry. In this paper, the numbers of lines and conics on various hypersurfaces which satisfy certain incidence properties are calculated, and shown to agree with the numbers pred...
1993-01-27
2008-02-03
[ "alg-geom", "hep-th", "math.AG" ]
Sheldon Katz
alg-geom/9301005
The topology of the space of rational curves on a toric variety
Let $X$ be a compact toric variety. Let $Hol$ denote the space of based holomorphic maps from $CP^1$ to $X$ which lie in a fixed homotopy class. Let $Map$ denote the corresponding space of continuous maps. We show that $Hol$ has the same homotopy groups as $Map$ up to some (computable) dimension. The proof uses a descr...
1993-01-24
2008-02-03
[ "alg-geom", "math.AG" ]
Martin A. Guest
alg-geom/9301004
The Geometry of Bielliptic Surfaces in P^4
In 1988 Serrano \cite{Ser}, using Reider's method, discovered a minimal bielliptic surface in $\PP^4$. Actually he showed that there is a unique family of such surfaces and that they have degree 10 and sectional genus 6. In this paper we describe, among other things, the geometry of the embedding of the minimal biellip...
1993-01-20
2008-02-03
[ "alg-geom", "math.AG" ]
A. Aure, W. Decker, K. Hulek, S. Popescu, K. Ranestad
alg-geom/9301002
Minimal Cohomology Classes and Jacobians
We show that on the Jacobian $(JC,\theta)$ of a smooth curve $C$ of genus $g$, any effective cycle in $JC$ with cohomology class $\theta^d/d!$ is a translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove that for $1<d<g$, the Jacobian locus (\resp the locus of intermediate Jacobians of cubic threef...
1993-01-06
2008-02-03
[ "alg-geom", "math.AG" ]
Olivier Debarre
alg-geom/9301003
Non-trivial Linear Systems on Smooth Plane Curves
Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically closed field $k$. A base point free complete very special linear system $g^r_n$ on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor $E$ on $C$ of degree $md-n$ such that $g^r_n=|mg^2_d-E|$ and $r=(m^2+3m)/2-(md-n)$. I...
1993-01-06
2008-02-03
[ "alg-geom", "math.AG" ]
Marc Coppens and Takao Kato